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Intro to Analysis Proof help

Hi, I'm self studying analysis, and I'm having problem with this proof. I've gotten most in my book so far but this has posed a problem.

I've attached the problem.

for part 1 I just said A is non empty since when x = 1/5 and n = 5 1 is an integer

for part 2 I let k = 1, x = 3/2 and showed that 1 < 3/2 < 2

For part 3 and 4 I have no idea what to do and i'm not sure whether i've done the prior correctly. I'd appreciate any help. Thanks!

Re: Intro to Analysis Proof help

Quote:

Originally Posted by

**glambeth** Hi, I'm self studying analysis, and I'm having problem with this proof. I've gotten most in my book so far but this has posed a problem.

I've attached the problem.

for part 1 I just said A is non empty since when x = 1/5 and n = 5 1 is an integer

Then you have misunderstood the whole thing! The theorem you are trying to prove is that "If p is the not the square of an integer and then x is irrational". You cannot just **choose** a value for x. x is "given" by . The crucial point here is "Assume that x is a positive rational number. What is the **definition** of "rational number"?

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for part 2 I let k = 1, x = 3/2 and showed that 1 < 3/2 < 2

Again, you cannot **assume** a value for x. x is given by and you must use that x.

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For part 3 and 4 I have no idea what to do and i'm not sure whether i've done the prior correctly. I'd appreciate any help. Thanks!

Re: Intro to Analysis Proof help

Re: Intro to Analysis Proof help

Wow! I misread that problem completely, I appreciate the help. I'll let you guys know if I have any problems with constructing my proof! Thanks again!

Re: Intro to Analysis Proof help

Could you explain how mx and mk are integers and why the last line is a contradiction?